# How do you solve x^3<=4x^2?

Jul 27, 2016

$x \le 4$.

The Interval Form $: x \in \left(- \infty , 4\right]$.

#### Explanation:

We rewrite the inequality as $4 {x}^{2} - {x}^{3} \ge 0 \Rightarrow {x}^{2} \left(4 - x\right) \ge 0$.

In this, since ${x}^{2} \ge 0 , \forall x \in \mathbb{R}$, we must have, $4 - x \ge 0$.

Therefore, $4 \ge x$, or,

$x \le 4$, and, in the Interval Form, $x \in \left(- \infty , 4\right]$.